Problem: Which of the following numbers is a multiple of 7? ${77,99,104,116,120}$
Explanation: The multiples of $7$ are $7$ $14$ $21$ $28$ ..... In general, any number that leaves no remainder when divided by $7$ is considered a multiple of $7$ We can start by dividing each of our answer choices by $7$ $77 \div 7 = 11$ $99 \div 7 = 14\text{ R }1$ $104 \div 7 = 14\text{ R }6$ $116 \div 7 = 16\text{ R }4$ $120 \div 7 = 17\text{ R }1$ The only answer choice that leaves no remainder after the division is $77$ $ 11$ $7$ $77$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $77$ $77 = 7\times11 7 = 7$ Therefore the only multiple of $7$ out of our choices is $77$. We can say that $77$ is divisible by $7$.